The present invention relates to the field of interval arithmetic processing circuitry and in particular relates to modal interval (MI) processors capable of performing reliable computations on MI data types.
Interval processors in the prior art are characterized by the exclusive implementation of set-theoretical interval arithmetic, the so-called “classical” interval arithmetic of Ramon Moore. The design of such processors is motivated by the fact that interval operations are more complex than traditional floating-point calculations.
There is a significant problem that none of the existing interval processor designs have considered. The problem is fundamental in the sense that it resides in the system of interval arithmetic itself. In 2001, a series of papers published by Miguel Sainz introduced a new type of mathematical interval known as “modal intervals.” These papers render obsolete all prior work in the field of interval processor design by redefining the fundamental notion of an interval. In one view, modal intervals are a generalization of set-theoretical intervals. Analysis of modal intervals shows that existing computing hardware based on set-theoretical interval functions is fundamentally flawed and lacking in completeness and correctness.
The following references are relevant to the understanding of modal intervals, modal interval mathematics, and the invention.
Set-Theoretical Intervals
    Jaulin, Luc, et. al., “Applied Interval Analysis,” Springer Verlag, 2001.    Hansen, Eldon and William Walster, “Global Optimization Using Interval Analysis,” 2nd ed., Marcel Dekker, 2004.    Moore, Ramon, “Interval Analysis,” Prentice Hall, 1966.Modal Intervals    Sainz, Miguel, et. al., “Ground Construction of Modal Intervals,” University of Girona, 2001.    Sainz, Miguel, et. al., “Interpretability and Optimality of Rational Functions,” University of Girona, 2001.    *Sainz, Miguel, et. al., “Modal Intervals,” Reliable Computing 7.2, 2001, pp. 77.    Sainz, Miguel, et. al., “Semantic and Rational Extensions of Real Continuous Functions,” University of Girona, 2001.
The web site having the URL of www.mice.udg.es/cgi-bin/ mi_fstar.cgi?t=1&h=1 at this time provides a web-based modal intervals calculator. The *Sainz article from Reliable Computing 7.2 is incorporated by reference into this specification.